Frontpage and articles/ category with different Layout

@Heinrich: This is quite different setup that you are trying to do it. Yes, this is possible.
Step 1: First create the page, and then in your right sidebar of edit page, you will see “Page Attributes”, where you need to assign template as “Blog Template”. Further, in your edit page, you will see Catch Box Options meta box where you can select sidebar layout to “Right sidebar”.
This make the page with right sidebar and latest articles.
Step 2: Now, you need to assign this page to Front page. Go to “Settings => Reading”. Then in “Front page displays”, you need to check on “A static page (select below)” and then select page that you have created in Step 1 as the Front Page.
Step3: Now to make all other pages different layouts, you can go to “Appearance => Theme Options => Default Layouts” and select the layout you want.

@Heinrich: Did you edit the file page-blog.php? Please restore that file and add the following CSS in “Appearance => Theme Options => Custom CSS” box to hide the page name.
.home .page-header { display: none; }